15. determine one positive and one negative coterminal angles for $752^{circ}$
16. determine one positive and one negative coterminal angle for $\frac{\pi}{14}$
give your answer in radians.
17. determine one positive and one negative coterminal angle for $415^{circ}$
18. rewrite the given angle in degree measure. $-\frac{11\pi}{6}$
a) $-660^{circ}$ b) $-330^{circ}$ c) $-300^{circ}$ d) $-315^{circ}$ e) $-345^{circ}$
19. rewrite the given angle in radian measure. $72^{circ}$
a) $\frac{7\pi}{5}$ b) $\pi$ c) $\frac{\pi}{5}$ d) $\frac{2\pi}{5}$ e) $\frac{3\pi}{5}$

Question

Accepted Answer

### 15. Determine one positive and one negative coterminal angles for $752^{\circ}$
# Explanation:
## Step1: Subtract $360^{\circ}$ to find a positive coterminal angle
$752^{\circ}- 360^{\circ}=392^{\circ}$
## Step2: Subtract $2\times360^{\circ}$ to find a negative coterminal angle
$752^{\circ}-2\times360^{\circ}=752^{\circ}-720^{\circ} = 32^{\circ}$, $32^{\circ}-360^{\circ}=-328^{\circ}$

# Answer:
One positive coterminal angle is $392^{\circ}$, one negative coterminal angle is $-328^{\circ}$

### 16. Determine one positive and one negative coterminal angle for $\frac{\pi}{14}$
# Explanation:
## Step1: Add $2\pi$ to find a positive coterminal angle
$\frac{\pi}{14}+2\pi=\frac{\pi + 28\pi}{14}=\frac{29\pi}{14}$
## Step2: Subtract $2\pi$ to find a negative coterminal angle
$\frac{\pi}{14}-2\pi=\frac{\pi-28\pi}{14}=-\frac{27\pi}{14}$

# Answer:
One positive coterminal angle is $\frac{29\pi}{14}$, one negative coterminal angle is $-\frac{27\pi}{14}$

### 17. Determine one positive and one negative coterminal angle for $415^{\circ}$
# Explanation:
## Step1: Subtract $360^{\circ}$ to find a positive coterminal angle
$415^{\circ}-360^{\circ} = 55^{\circ}$, $55^{\circ}+360^{\circ}=415^{\circ}$ (already used, so $415^{\circ}+360^{\circ}=775^{\circ}$)
## Step2: Subtract $2\times360^{\circ}$ to find a negative coterminal angle
$415^{\circ}-2\times360^{\circ}=415^{\circ}-720^{\circ}=-305^{\circ}$

# Answer:
One positive coterminal angle is $775^{\circ}$, one negative coterminal angle is $-305^{\circ}$

### 18. Rewrite the given angle $-\frac{11\pi}{6}$ in degree measure
# Explanation:
## Step1: Use the conversion formula $\theta_{deg}=\theta_{rad}\times\frac{180^{\circ}}{\pi}$
$-\frac{11\pi}{6}\times\frac{180^{\circ}}{\pi}=- 330^{\circ}$

# Answer:
B. $-330^{\circ}$

### 19. Rewrite the given angle $72^{\circ}$ in radian measure
# Explanation:
## Step1: Use the conversion formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180^{\circ}}$
$72^{\circ}\times\frac{\pi}{180^{\circ}}=\frac{72\pi}{180}=\frac{2\pi}{5}$

# Answer:
D. $\frac{2\pi}{5}$

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QUESTION IMAGE

Question

Explanation:

15. Determine one positive and one negative coterminal angles for \(752^{\circ}\)

Step1: Subtract \(360^{\circ}\) to find a positive coterminal angle

Step2: Subtract \(2\times360^{\circ}\) to find a negative coterminal angle

Step1: Add \(2\pi\) to find a positive coterminal angle

Step2: Subtract \(2\pi\) to find a negative coterminal angle

Step1: Subtract \(360^{\circ}\) to find a positive coterminal angle

Step2: Subtract \(2\times360^{\circ}\) to find a negative coterminal angle

Answer:

16. Determine one positive and one negative coterminal angle for \(\frac{\pi}{14}\)